Monday, August 16, 2004

Watching the Olympics, I began to wonder: How often should we expect athletes to set new world records? After all, records get broken during every Olympic Games, and in other competitions each year. Are we (by “we” I mean humankind) breaking them quickly, slowly, or at about the normal rate? How would we know whether the number of new records exceeded our justifiable expectations?

Some a priori theorizing. Suppose the population of the earth is constant (death rate equals birth rate). We can think of each new athlete’s performance in some event – say, the 100-yard dash – as a draw from a distribution (probably a bell curve) of relevant skills. The current world record is a mark somewhere toward the right end of the bell curve. The chance of any new athlete being able to break the record is equal to the area in the right tail of the distribution (under the curve, to the right of the current record). Each time someone sets a new record, the mark moves to the right, and therefore the area in the right tail shrinks. Therefore, given a constant number of new athletes each year, each new record diminishes the probability of another new record in any subsequent year. (A constant number of new athletes means we have the same number of draws from the distribution each year, but the smaller tail results in a smaller likelihood of any new athlete setting a new record.) Hence, world records should be set less and less often.

I can think of two major factors that could alter the conclusion. First, a growing population implies more draws at the distribution each year. Second, improvement in health and training technology could shift the whole curve to the right, thereby increasing the area in the right tail. These effects would both offset, possibly even overcome, the predicted slow-down described above.

So what’s the reality? Is the average time it takes for an old record to get replaced by a new one growing, shrinking, or remaining constant? A quick Google search turned up nothing – but admittedly, I didn’t search long. I encourage anyone with actual data to forward it to me.